This assignment consists of three parts.  Parts  1, 2 and 3 are worth 40,  10 and 50  marks, respectively.

Your report should be submitted as a PDF document, consisting of no more than 1,500 words. The word count covers the main body of text, including in-text citations and direct quotations, and excludes equations, figures, charts, tables, footnotes, reference list and bibliography.

Please do not include an appendix, and please do not submit an Excel spreadsheet.

Part 1 – Umbrella

Umbrella is an agrochemical company that produces and distributes worldwide. Currently, they are restructuring the production of one of their fertilizers, named Growell. To produce Growell efficiently, Umbrella uses the batch approach, in which a certain number of litres is produced at one time. This reduces setup costs and allows Umbrella to produce Growell at a competitive price. Unfortunately, Growell loses some of its properties with time.

Umbrella produces Growell in batches of 20,000 litres, 30,000 litres and 40,000 litres. For simplicity, assume that in the coming three-month planning period, Umbrella will sell either 20,000 litres, 30,000 litres or 40,000 litres. More specifically, using historical data, Umbrella estimates that there is an equal probability of selling 20,000 litres, 30,000 litres or 40,000 litres.

The question Umbrella is facing is how many litres to produce of Growell in the next batch run.  Growell  sells  for  £10  per  litre.  Manufacturing  costs  amount  to  £5.50  per  litre,  and handling costs and warehousing costs are estimated to be £0.50 per litre. Umbrella allocates advertising costs to Growell at £1.50 for each litre that it produces. If Growell is not sold within three months, the fertilizer loses some of its properties. It can, however, be sold at a salvage value, estimated to be £5 per litre. Furthermore, Umbrella has guaranteed to its suppliers that there will always be an adequate supply of Growell. If Umbrella does run out, it has agreed to purchase a comparable fertilizer from a competitor at £12 per litre. No handling or warehousing costs are incurred on fertilizer provided by the competitor.

(a) Use a decision tree to identify the best decision for Umbrella. (10 marks)

(b) How does your answer to part (a) change with respect to changes in the salvage value and demand probabilities? (20 marks)

(c) What is the most that Umbrella should pay for information regarding the level of demand? (10 marks)